Knowing the large-scale flows that occur in the upper convection zone is
critical to our understanding of the processes that govern the solar
cycle. Here we apply solar oscillation ring-diagram analysis to
several small tracked regions on the sun, approximately 15^\circ on a
side, as they rotate across the solar disk, in order to determine the
persistence and depth variation of the large-scale flows beneath these
regions. We use the Doppler velocity images from the Michelson Doppler
Imager (MDI) instrument aboard the Solar Heliospheric Observatory
(SOHO) satellite using quiet-sun data taken during the MDI Dynamics
campaign of 1996. Three regions at different latitudes were extracted
from full-disk Doppler images of 1024 \times 1024 pixels (pixel size
\sim 2'' square) with a one-minute temporal cadence. Eight
sequential 1536-minute time intervals were tracked, remapped onto
great-circle grids, spatially and temporally filtered, and apodized in
space and time. They were then Fourier transformed in two spatial
dimensions and time. The resulting power spectra show characteristic
rings at each frequency slice. Shifts in the center positions of the
rings are caused by underlying flow fields and can be inverted to map
these flows with depth. We use several techniques to fit these shifts
in order to assess the stability of the results.